This application is related to and incorporates by reference Japanese Patent Application No. 2001-113081, which was filed on Apr. 11, 2001.
The present invention relates to a vibration type angular velocity sensor in which, when angular velocity is applied, the applied angular velocity is detected based on a change in capacitance between a vibrator and a detecting electrode. The change in capacitance is caused by the vibration of the vibrator.
A related angular velocity sensor has a base, a vibrator, which is supported by the base via a spring portion, and a detecting electrode opposed to the vibrator. This sensor detects angular velocity such that, when angular velocity is applied to the sensor when the vibrator is vibrating in a first direction, which is a driving vibration, the vibrator vibrates in a second direction, which is a detecting vibration that is perpendicular to the first direction, and the applied angular velocity is detected based on a change in capacitance between the vibrator and the detecting electrode.
In such a vibration type angular velocity sensor, as shown in the following mathematical expression A, detecting sensitivity S is proportional to resonance magnification xcex2, which is determined by the resonance frequency (actual vibration frequency of the vibrator) fd in a driving vibration mode, a resonance frequency fs in a detecting vibration mode, and a value Qs in the detecting vibration mode.       S    ⁢          xe2x80x83        ∝          xe2x80x83        ⁢    β    =      1                                        {                          1              -                                                (                                                            f                      ⁢                                              xe2x80x83                                            ⁢                      d                                                              f                      ⁢                                              xe2x80x83                                            ⁢                      s                                                        )                                2                                      }                    2                +                              (                                          f                ⁢                                  xe2x80x83                                ⁢                d                                            f                ⁢                                  xe2x80x83                                ⁢                                  s                  ·                  Q                                ⁢                                  xe2x80x83                                ⁢                s                                      )                    2                    
where Qs in expression A is given by the following expression B:       Q    ⁢          xe2x80x83        ⁢    s    =                    m        ⁢                  xe2x80x83                ⁢        k              c  
in which m is the mass of the vibrator, k is the spring constant of a spring device in the detecting vibration mode, and c is an attenuation coefficient of the vibrator in the detecting vibration mode.
The attenuation coefficient c has temperature characteristics, and when the sensor is operated in the atmosphere, the attenuation coefficient c is increased by the effect of air damping (flow resistance of air) in the vicinity of the vibrator, and thus the detecting sensitivity S varies according to temperature.
The related angular velocity sensor is generally packaged in a vacuum and operated in a vacuum (for example, about 200 Pa) and is thus little affected by air damping. In other words, under such a vacuum, the attenuation coefficient c is reduced to a small value, and thus Qs is large, according to the mathematical expression B. This makes the second term, which includes Qs, in the denominator of mathematical expression A so small that it is negligible, as compared with the first term, and therefore temperature variation in the detecting sensitivity is hardly caused by air damping.
However, producing such a vacuum package presents complicated problems and takes a great amount of time and labor.
It is an object of the present invention to suppress temperature variation caused by air damping in the detecting sensitivity of a vibration type angular velocity sensor that that operates in the atmosphere.
In order to reduce the temperature variation in the detecting sensitivity caused by the air damping, it can be seen from expression A that the rate of change due to the temperature of the resonance magnification xcex2 should be reduced. To be more specific, it was found that making the rate of change due to the temperature of the resonance magnification xcex2 not larger than 1% in the working temperature range of the sensor (from xe2x88x9240xc2x0 C. to +85xc2x0 C.) suppresses the temperature variation, caused by air damping, in the detecting sensitivity to a very small level, at which there is no significant problem in practical use.
It was noticed that the attenuation coefficient c varies according to the temperature and that the effect of the second term {fd/(fsxc2x7Qs)}2 in the square root symbol of the denominator in mathematical expression A showing the resonance magnification xcex2 was to be reduced.
Since the value Qs is essentially determined by the structure of the sensor device (shapes of the vibrator and the detecting electrode), it was decided to control the ratio of the resonance frequency fd in the driving vibration mode to the resonance frequency fs in the detecting vibration mode (hereinafter, fd/fs is referred to as the degree of detuning xcex1).
According to the analysis of the present inventor, the value Qs in the detecting vibration mode varies from +25% to xe2x88x9215% in the working temperature range from xe2x88x9240xc2x0 C. to +85xc2x0 C. The degree of detuning xcex1 is found by analysis such that the rate of change of the resonance magnification xcex2 is suppressed to a value not larger than 1% even if Qs varies from +25% to xe2x88x9215%.
The invention has been made based on the result of this analysis and is characterized in that, in a vibration system having spring devices (33, 34) and a vibrator (31), the degree of detuning xcex1 (xcex1=fd/fs), that is, the ratio of a resonance frequency fd in the driving vibration to a resonance frequency fs in the detecting vibration and a Q value in the detecting vibration Qs satisfy the relationship expressed by the following mathematical expression C:   α  ≥            5.720      xc3x97                        10                      -            9                          ·        Q            ⁢              xe2x80x83            ⁢              s        6              -          1.012      xc3x97                        10                      -            6                          ·        Q            ⁢              xe2x80x83            ⁢              s        5              +          7.102      xc3x97                        10                      -            5                          ·        Q            ⁢              xe2x80x83            ⁢              s        4              -          2.517      xc3x97                        10                      -            3                          ·        Q            ⁢              xe2x80x83            ⁢              s        3              +          4.736      xc3x97                        10                      -            2                          ·        Q            ⁢              xe2x80x83            ⁢              s        2              -          4.549      xc3x97                        10                      -            1                          ·        Q            ⁢              xe2x80x83            ⁢      s        +    2.923  
If xcex1 and Qs satisfy the above relationship, the rate of change in the resonance frequency xcex2 is no larger than 1% in the working temperature range of the sensor from xe2x88x9240xc2x0 C. to +85xc2x0 C. Therefore, it is possible to provide a vibration type angular velocity sensor in which temperature variation in the detecting sensitivity caused by air damping is suppressed to a very small level such that there is no significant problem in practical use when the sensor is operated in the atmosphere.
Further, according to another aspect of the invention, in minimizing the rate of change, due to temperature variation, of the resonance magnification xcex2, it was found that, in expression A, the first term {1xe2x88x92(fd/fs)2}2 in the square root symbol of the denominator should be no smaller than 100 times the second term {fd/(fsxc2x7Qs)}2.
In another aspect, the invention is characterized in that, in a vibration system having the spring devices (33, 34) and the vibrator (31), the degree of detuning xcex1 and Qs satisfy the relationship expressed by the following expression D:
xcex14xe2x88x92(2+100/Qs2)xc3x97xcex12+1xe2x89xa70 
Also according to this relationship, temperature variation, caused by air damping, in the detecting sensitivity can be reduced to the extent that there is no significant problem in practical use when the vibration type angular velocity sensor is operated in the atmosphere.
The opposed portions of the detecting electrode and the vibrator can be made such that the detecting electrode (40) has a comb-like part, and the vibrator (31) has a comb-like part (35), and teeth, or projections, of the two comb-like parts are opposed to and interdigitated with each other.
Further, the base (20), the spring devices (33, 34), the vibrator (31) and the detecting electrode (50) are formed of semiconductor material.
The reference numerals in the parentheses above are exemplary and correspond to specific parts described below.